On the overdetermined system about surfaces with parallel mean curvature vector field.
type: Item
instance of: scholarly article
title: On the overdetermined system about surfaces with parallel mean curvature vector field.
zbMATH Open document ID: 1119.53312
author: Shinya Hirakawa
published in: Kodai Mathematical Journal
publication date: 2002-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kmj/1071674458
review text: The author studies two-dimensional surfaces embedded in a two-dimensional complex space form. Due to \textit{T. Ogata} [see Kodai Math. J. 18, No. 3, 397--407 (1995; Zbl 0865.53007)] the property that such an immersion has a parallel mean curvature vector field is equivalent to the existence of a certain overdetermined system \(S\) of differential equations. All solutions of the system \(S\) were given by \textit{K. Kenmotsu} and \textit{D. Zhou} [Am. J. Math. 122, 295--317 (2000; Zbl 0997.53006)]. In the present paper the author constructs the solutions of \(S\) by a different method which also uses the theory of polynomials.
reviewed by: Anton Gfrerrer
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1910498
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: complex space forms
zbMATH Keywords: mean curvature
MaRDI profile type: Publication
OpenAlex ID: W2026266053
DOI: 10.2996/KMJ/1071674458
description: scientific article; zbMATH DE number 1910498